# How do you find the complex conjugate of 3i?

Nov 29, 2015

The complex conjugate of $3 i$ is $\left(- 3 i\right)$

#### Explanation:

The complex conjugate of a number is another number with a real component equal to the original number and an imaginary component equal in magnitude but with the opposite sign.

$\textcolor{red}{\text{real")+color(blue)("imaginary}}$

$\textcolor{b l u e}{3 i} = \textcolor{red}{0} + \textcolor{b l u e}{3 i}$

So the complex conjugate is
$\textcolor{red}{0} + \textcolor{b l u e}{\left(- 3 i\right)} = \textcolor{b l u e}{- 3 i}$